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Chapter 33: Optics
Wavefronts and Rays • When light or other electromagnetic waves interact with
systems much larger than the wavelength, it’s a good approximation to • Neglect the wave nature of light. • Consider that the light travels in straight lines, called rays, while
in a uniform medium. • Rays are perpendicular to the wavefronts and the rays’ direction is that of
the wave propagation. • The ray approximation is also known as geometrical optics.
Reflection • When light reflects from a surface, the incident and reflected rays
make the same angle with the normal to the surface. • For smooth surfaces, parallel rays all reflect at the same angle. • The angles are equal (locally) even for rough surfaces.
• But because of the roughness, the light comes off in random directions. • This is called diffuse reflection.
The Plane Mirror
Question • You would like to buy a full-length mirror which allows
you to see yourself from head to toe. The minimum height of the mirror is A) half your height. B) two-thirds of your height. C) equal to your height. D) depends on distance you stand from mirror
Refraction • Refraction is the bending of light as it crosses the interface
between two different transparent media. • Refraction occurs because the wave
speed differs in different media. • For light, the index of refraction n
describes the speed change. • The speed of a wave in a medium is
v = c/n. • The angles of incidence and refraction
are related by Snell’s law: n1 sin ✓1 = n2 sin ✓2
Derivation of Snell’s Law �1
x
= sin ✓1
�2
x
= sin ✓2
�i = �tc/ni
�t c
n1 sin ✓1=
�t c
n2 sin ✓2
n1 sin ✓1 = n2 sin ✓2
�1
sin ✓1=
�2
sin ✓2
Clicker question • The figure shows the path of a light ray through three
different media. Rank the media in order of their refractive indices.
A. B. C. D.
1 2 3n n n> >
3 1 2n n n> >
3 2 1n n n> >
2 1 3n n n> >
Example: Sunlight strikes the surface of a lake. A diver sees the Sun at an angle of 42.0° with respect to the vertical. What angle do the Sun’s rays in air make with the vertical?
surface n1 = 1.00; air
n2 = 1.33; water
Normal
42°
Transmitted wave
incident wave
θ1
Example: Sunlight strikes the surface of a lake. A diver sees the Sun at an angle of 42.0° with respect to the vertical. What angle do the Sun’s rays in air make with the vertical?
surface n1 = 1.00; air
n2 = 1.33; water
Normal
42°
Transmitted wave
incident wave
θ1
( ) ( )
°=
=
°=
=
1.638920.0sin
42sin333.1sin00.1sinsin
1
1
1
2211
θ
θ
θ
θθ nn
Question 23.8 Gone Fishin’ I
To shoot a fish with a gun, should you aim directly at the
image, slightly above, or slightly below?
1) aim directly at the image
2) aim slightly above
3) aim slightly below
From:http://www.physicsclassroom.com/class/refrn/Lesson-1/Refraction-and-Sight
Mirages
Total internal reflection • The angle of incidence for when the angle of refraction is
90° is called the critical angle.
1
2
221
2211
sin
90sinsinsinsin
nn
nnnnn
c
c
=
=°=
=
θ
θ
θθ
• If the incidence angle is greater than the critical angle, the beam can not refract but is completely reflected
Fiber Optics
Dispersion • Index of refraction depends on wavelength
• If a beam of white light is incident on silicate glass (say with θinc=45°) which color bends more (due to refraction)?
1. blue
2. yellow
3. red
4. all refract the same
Polarization
http://webphysics.davidson.edu/physlet_resources/dav_optics/examples/polarization.html
Polarizers
For unpolarized light: Itransmitted = Iincident < cos
2✓ >=
1
2Iincident
• Poloroid filter: Electric field does work on electrons along strands of filter, causing E field in that direction to be attenuated
An unpolarized beam of light passes through 2 Polaroid filters oriented at 45o with respect to each other. The intensity of the original beam is Io. What is the intensity of the light coming through both filters?
A: (1/1.4)Io B: (1/2)Io C: (1/4)Io D: (1/8)Io E: None of the above
Io
c
Clicker Question
Unpolarized light, traveling in the direction shown, is incident on polarizer 1. Does any light emerge from polarizer 3?
A. Yes.
B. No.
QuickCheck 34.9
Example of Polarized Light: • Scattering of sunlight:
Example of Polarized Light: • Reflected light from medium with
higher index of refraction: • Reflected light is more polarized
with electric field parallel to the surface